Auctioneers may wish to sell related but different indivisible goods in
a single process. To develop such techniques, we study the geometry of
how an agent's demanded bundle changes as prices change. This object
is the convex-geometric object known as a `tropical hypersurface'.
Moreover, simple geometric properties translate directly to economic
properties, providing a new taxonomy for economic valuations. When
considering multiple agents, we study the unions and intersections of
the corresponding tropical hypersurfaces; in particular, properties of
the intersection are deeply related to whether competitive equilibrium
exists or fails. This leads us to new results and generalisations of
existing results on equilibrium existence. The talk will provide an
introductory tour to relevant economics to show the context of these
applications of tropical geometry. This is joint work with Paul
Klemperer.